Newborn Elephant Weights. New born elephant calves usually weigh between 200 and 250 pounds until october 2006, that is. an asian elephant at the Houston (Texas) zoo gave birth to a male calf weighing in at a whopping 384 pounds! Mack (like the truck) is believed to believed to be the heaviest elephant calf ever born at a facility accredited by the association of zoos and aquariums. If, indeed, the mean weight for new born elephant calves is 225 pounds with a standard deviation of 45 pounds, what is the probability of a newborn weighing at least 384 pounds? Assume that the weights of newborn elephants are normally distributed.

#### Solution

Let $X$ denote the weight for newborn calves.

Given that $X\sim N(225, 45^2)$. That is $\mu= 225$ and $\sigma =45$.

We want to find the probability of a newborn weighing at least 384 pounds.

The $Z$ score corresponding to $384$ is

` $$ \begin{aligned} z&=\frac{384-\mu}{\sigma}\\ &=\frac{384 - 225}{45}\\ &= 3.53 \end{aligned} $$ `

The probability of a newborn weighing at least 384 pounds is

` $$ \begin{aligned} P(X\geq 384) &= 1-P\bigg(\frac{X-\mu}{\sigma} < \frac{384-225}{45}\bigg)\\ &= 1-P\bigg(Z < 3.53\bigg)\\ &=1-0.9998\\ &=0.0002 \end{aligned} $$ `

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators